A199333 Triangle read by rows: T(n,0) = T(n,n) = 1, 0 < k < n: T(n,k) = smallest prime not less than T(n-1,k) + T(n-1,k-1).
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 7, 5, 1, 1, 7, 13, 13, 7, 1, 1, 11, 23, 29, 23, 11, 1, 1, 13, 37, 53, 53, 37, 13, 1, 1, 17, 53, 97, 107, 97, 53, 17, 1, 1, 19, 71, 151, 211, 211, 151, 71, 19, 1, 1, 23, 97, 223, 367, 431, 367, 223, 97, 23, 1, 1, 29, 127
Offset: 0
Examples
0: 1 1: 1 1 2: 1 2 1 3: 1 3 3 1 4: 1 5 7 5 1 5: 1 7 13 13 7 1 6: 1 11 23 29 23 11 1 7: 1 13 37 53 53 37 13 1 8: 1 17 53 97 107 97 53 17 1 primes in 8th row: T(7,0) + T(7,1) = 1+13 = 14 --> T(8,1) = T(8,7) = 19; T(7,1) + T(7,2) = 13+37 = 50 --> T(8,2) = T(8,6) = 53, already in row 7; T(7,2) + T(7,3) = 37+53 = 90 --> T(8,3) = T(8,5) = 97; T(7,3) + T(7,4) = 53+53 = 106 --> T(8,4) = 107.
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Programs
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Haskell
a199333 n k = a199333_tabl !! n !! k a199333_row n = a199333_tabl !! n a199333_list = concat a199333_tabl a199333_tabl = iterate (\row -> map a159477 $ zipWith (+) ([0] ++ row) (row ++ [0])) [1]
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Mathematica
T[n_, k_] := T[n, k] = Switch[k, 0|n, 1, _, With[{m = T[n-1, k] + T[n-1, k-1]}, If[PrimeQ[m], m, NextPrime[m]]]]; Table[T[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 19 2021 *)
Formula
T(n,k) = A007918(T(n-1,k) + T(n-1,k-1)), 0 < k < n, T(n,0) = T(n,n) = 1.
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